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• Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning [pdf]

Yuhua Zhu, Yuming Paul Zhang, Haoyu Zhang.

Preprint, 2025.

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• Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimization [pdf]

Nicolás García Trillos, Aditya Kumar Akash, Sixu Li, Konstantin Riedl, Yuhua Zhu*.

Philosophical Transactions A, to appear, 2025.

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• CB2O: Consensus-Based Bi-Level Optimization [pdf]

Nicolás García Trillos, Sixu Li, Konstantin Riedl, Yuhua Zhu*.

Preprint, 2025.

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• On Bellman Equations for Continuous-time Policy Evaluation: High-order Discretization and Function Approximation [pdf]

Wenlong Mou, Yuhua Zhu*.

Preprint, 2024.

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• PhiBE: A PDE-based Bellman Equation for Continuous Time Policy Evaluation [pdf]

Yuhua Zhu.

Preprint, 2024.

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• An Interacting Particle Consensus Method for Constrained Global Optimization [pdf]

Jose Carrillo, Shi Jin, Haoyu Zhang, Yuhua Zhu*.

Preprint, 2024.

Matlab code

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• FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization. [pdf]

Jose A. Carrillo, Nicolas Garcia Trillos, Sixu Li, Yuhua Zhu*.

Journal of Machine Learning Research (JMLR), 2024.

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• Continuous-in-time Limit for Bayesian Bandits. [pdf]

Yuhua Zhu, Zachary Izzo and Lexing Ying.

Journal of Machine Learning Research (JMLR), 2024.

Matlab code

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• Operator Augmentation for Model-based Policy Evaluation. [pdf]

Xun Tang, Lexin Ying and Yuhua Zhu*.

Communications in Mathematical Sciences, 2023.​

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• Variational Actor-Critic Algorithms. [pdf]

Yuhua Zhu and Lexing Ying.​

ESAIM: Control, Optimisation and Calculus of Variations, 2023.

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• A Note on Optimization Formulations of Markov Decision Processes. [pdf]

Lexing Ying and Yuhua Zhu.​

Communications in Mathematical Sciences, 20(3):727–745, 2022.

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• The Vlasov Fokker Planck Equation with High Dimensional Parametric Forcing Term. [pdf]

Shi Jin, Yuhua Zhu*, and Enrique Zuazua. 

Numerische Mathematik, 150(2):479–519, 2022.

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• Borrowing From the Future: Addressing Double Sampling in Model-free Control. [pdf]

Yuhua Zhu, Zachary Izzo and Lexing Ying

Mathematical and Scientific Machine Learning, pages 1099–1136, PMLR, 2022.

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• Why Resampling Outperforms Reweighting for Correcting Sampling Bias with Stochastic Gradients. [pdf]

Jing An, Lexing Ying, Yuhua Zhu*.

International Conference on Learning Representations (ICLR), 2021.

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• A Sharp Convergence Rate for a Model Equation of the Asynchronous Stochastic Gradient Descent. [pdf]

Yuhua Zhu, Lexing Ying.​ 

Communications in Mathematical Sciences, 19(3), 851-863, 2020.

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• Borrowing From the Future: An Attempt to Address Double Sampling. [pdf]

Yuhua Zhu and Lexing Ying.

Mathematical and Scientific Machine Learning, PMLR 107:246-268, 2020. 

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• On Large Batch Training and Sharp Minima: A Fokker-Planck Perspective. [pdf]

Xiaowu Dai and Yuhua Zhu*.

Journal of Statistical Theory and Practice (JSTP), special issue on "Advances in Deep Learning", 2020. 

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• A Consensus-Based Global Optimization Method for High Dimensional Machine Learning Problems. [pdf]

Jose Carrillo, Shi Jin, Lei Li and Yuhua Zhu*

ESAIM: Control, Optimisation and Calculus of Variations 27, S5, 2020.

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• A Local Sensitivity and Regularity Analysis for the Vlasov-Poisson-Fokker-Planck System with Multi-dimensional Uncertainty and the Spectral Convergence of the Stochastic Galerkin Method. [pdf]

Yuhua Zhu. 

Networks and Heterogeneous Media, 14(4), 677-707, 2019.

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• An Uncertainty Quantification Approach to the Study of Gene Expression Robustness. [pdf]

Pierre Degond, Shi Jin and Yuhua Zhu*.

Methods and Applications of Analysis (A special issue in honor of the 80th birthday of Prof. Ling Hsiao), 2019.

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• Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales. [pdf]

Shi Jin and Yuhua Zhu*. 

SIAM Journal on Mathematical Analysis, 50, 1790-1816, 2018.

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• The Vlasov-Poisson-Fokker-Planck System with Uncertainty and a One-Dimensional Asymptotic-Preserving Method. [pdf]

Yuhua Zhu and Shi Jin.

SIAM Multiscale Modeling and Simulation, 15, 1502-1529, 2018.

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*: Alphabetical authorship.

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